2D Random Walk

Steps: 0
Mean r²: 0
4Dt fit:
Random walk: each step moves ±dx or ±dy with equal probability. Mean-square displacement ⟨r²⟩ = 4Dt grows linearly with time t (steps). This is the 2D diffusion law with D = σ²/2. Einstein (1905): Brownian motion is random walks at molecular scale. The MSD chart shows 4Dt prediction vs actual.